Mass of Nows: A Geometric Theory of Inertia and Gravity

Abstract. We propose that inertial and gravitational mass arise from a single geometric mechanism: the resistance a particle encounters when its worldline is forced to cross successive “now-slices” of spacetime. These slices are required by the relativity of simultaneity. A particle at rest crosses one slice per Planck time; acceleration tilts its worldline, increasing the number of slices crossed per unit coordinate time, and the accumulated resistance is inertial mass. Gravity is the same resistance, since a mass curves spacetime and the particle must traverse the already-tilted slices. Light, having a null worldline, crosses no slices and therefore experiences no drag — which is why it moves at c with nothing to slow it. No messenger particle is required.

Postulates.

1. The relativity of simultaneity requires an infinite number of now-slices through spacetime.
2. Every particle exists in all now-slices, by virtue of its wave function permeating four-dimensional spacetime.
3. Viewed from a single now-slice, the four-dimensional wave appears as a particle.
4. Acceleration tilts the particle’s now-slice, causing it to cross more slices per second of coordinate time.
5. The resistance encountered crossing each slice is the source of inertial mass.
6. Gravity is the identical resistance: a mass warps spacetime, and any mass passing through the warped region crosses more slices per second.
7. All mass moves through spacetime at the speed of light; the warping of spacetime is the equal-and-opposite reaction required by Newton’s third law.

Derivation. The number of now-slices crossed per unit coordinate time is fixed by the metric — it is the tilt of the worldline against the slice normal, a pure function of velocity. The drag coefficient is therefore not free; its functional form is locked to the Lorentz factor. As velocity approaches c, the tilt approaches ninety degrees, the number of slices crossed diverges, and the resistance becomes infinite. This reproduces the relativistic mass curve and the hard light-speed limit without additional postulates. A photon, having zero proper time, crosses no slices and feels no drag — consistent with observation.

Consequences.

• Inertia and gravity are the same phenomenon, counted in now-slices crossed. This is the equivalence principle derived, not assumed.
• There is no collapse of the wave function. The wave exists in all slices; a measurement selects the slice from which it is read. This replaces the measurement problem with geometry.
• Quantum indeterminacy follows: a particle has no absolute location, only a location relative to a now-slice. The slice is the reference that defines position.
• No graviton is required. Gravity is the geometry of the slices, not a force mediated by a particle.
• The Higgs mechanism may still account for rest mass, but inertia — the resistance to acceleration — is explained here without it.

Open questions. The magnitude of inertial mass is not yet derived from first principles; the theory predicts the shape of the velocity-dependent curve but imports the overall scale. Deriving that scale — whether from vacuum energy density or from the geometry of the now-slice itself — is the central remaining calculation. Additionally, whether the Born rule for measurement probabilities falls out of the slice geometry, rather than being postulated, remains to be shown.

Conclusion. If the shape of the relativistic mass curve can be shown to follow from the geometry of now-slices alone, with no fitted parameters, the theory offers a unified, messenger-free account of inertia and gravity grounded entirely in established relativity and the existence of a nonzero vacuum energy. The logic holds with the minimal assumption that the drag per slice is nonzero; the magnitude is a separate question the theory does not need to answer in order to be relevant.